Least Common Multiple (LCM) of 111 and 167
The least common multiple (LCM) of 111 and 167 is 18537.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 111 and 167?
First, calculate the GCD of 111 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 167 = 0 remainder 111 |
| 2 | 167 ÷ 111 = 1 remainder 56 |
| 3 | 111 ÷ 56 = 1 remainder 55 |
| 4 | 56 ÷ 55 = 1 remainder 1 |
| 5 | 55 ÷ 1 = 55 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 80 | 4720 |
| 17 and 21 | 357 |
| 12 and 156 | 156 |
| 193 and 145 | 27985 |
| 71 and 73 | 5183 |